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CIRCLES & STRAIGHT LINES
1.
The radius of the circle 3x2 + 3y2 + 6x – 12y – 1 = 0 is
a) 11
2.
b)
b) 10
5.
7.
8.
d) 6
c) 3
2
d) 4
2
2
2
The radical axis of the circles x + y + 3x + 4y – 5 = 0 and x + y – 5x + 5y – 6 = 0 is
a) 8y – x + 1 = 0
b) 8x – y + 1 = 0
c) 8x – 8y + 1 = 0
d) y - 8x +1= 0
The length of the tangent drawn from the point (1,3) to the circle x2 + y2 – 2x + 4y – 11 = 0
is
b) 2
c) 3
d) 4
The equation of the circle with centre at (4, 1) and having 3x + 4y – 1 = 0 as tangent is
a) x2+y2 – 8x-2y -8 =0
b) x2 + y2 – 8x – 2y + 8 =0
c) x2 +y2 – 8x + 2y + 8 = 0
d) x2 + y2- 8x – 2y + 4 = 0
The equation of the circle passing through (2, 1) and touching the coordinate axes is
a) x2 + y2 – 2x – 2y + 1 = 0
b) x2 + y2 + 2x + 2y + 1 = 0
c) x2 + y2 – 2x – 2y – 1 = 0
d) x2 + y2 + 2x + 2y – 1 = 0
The line x + y + 1 = 0 touches the circle x2 + y2 – 3x + 7y + 14 =0 then the point of contact
is
a) (1, 0)
9.
c)8
b) 2
a) 1
6.
d) 20
The number of circles that touch all the lines x+y-4 = 0, x-y+2 = 0 and y = 2 is
a) 1
4.
4
3
c)
The length of the intercept made by the circle x2 + y2 – 12x + 14y + 11 = 0 on the x-axis is
a) 9
3.
19
2
b) (2, -3)
c) (5, 2)
2
d) (-1, 0)
2
The length of tangent from a point on the circle x + y + 4x – 6y – 12 = 0 to the circle
x2 + y2 + 4x – 6y + 4 = 0 is
a)
4
b) 12
c) 15
2
d) 8
2
10. If the length of tangent from (2, 3) to the circle x + y + 6x + 2ky–6=0 is equal to 7, then
k=
a) 2
b) 4
2
c) 5
2
2
d) 7
2
11. If the circles x + y + 2x – 4y + 4 = 0 and x + y - 2x – 4y – 4 = 0 touch each other then
equation of common tangent is
a) x – 2 = 0
b) x + 2 = 0
2
2
c) y = 0
2
2
d) y + 1 = 0
2
12. If two circles (x – 1) + (y – 3) = r and x + y - 8x + 2y + 8 = 0 intersect in two distinct
points then
a) r < 2
b) r = 2
c) r > 2
d) 2< r < 8
13. The lines 2x – 3y – 5 = 0 and 3x – 4y – 7 = 0 are diameters of a circle having area 154 sq
units then the equation of the circle is
a) x2 + y2 + 2x – 2y – 62 = 0
b) x2 + y2 + 2x – 2y – 47 = 0
c) x2 + y2 - 2x + 2y – 47 = 0
d) x2 + y2 - 2x + 2y – 62 = 0
1
14. The radius of the circle passing through the point (6, 2) and two of whose diameters are
x + y = 6 and x + 2y = 4 is
a) 4
b) 6
d) 20
d)
20
15. Length of the chord cut off by y = 2x + 1 from the circle x2 + y2 = 2 is
a)
5
6
b)
6
5
c)
6
5
d)
5
6
16. The line 3x – y + K = 0 is a tangent to the circle 5x2 + 5y2 – 35 = 0 them K =
a)
b) 70
70
c) 21
d) 35
17. The equation of the circle with centre at (-4, 3) and touching the line 5x – y – 3 = 0 is
a) x2 + y2 - 4x + 6y – 1 = 0
b) x2 + y2 + 8x – 6y – 1 = 0
c) x2 + y2 + 4x – 6y – 1 = 0
d) x2 + y2 - 8x + 6y – 1 = 0
18. If the circles 3x2 + 3y2 + 3x + 9y –K=0 and 4x2 + 4y2 – 4x + 2y +K=0 are orthogonal them
K=
a) 3
b) -3
2
c) 2
d) 0
2
19. If the circle x + y + px – qy + c = 0 touches the x – axis then
a) p2 = c
b) p2 = 4c
c) q2 = 4c
d) q2 = c
20. The circumference of the circle x2 + y2 – 4x sin T - 4y cos T - 12 = 0 is
a) 2S
b) 3S
c) 4S
d) 8S
21. The equation of the circle passing through the origin and cutting off intercepts 5 and 6 on the
positive side of the axes respectively is
b) x2 + y2 - 5x + 6y = 0
a) x2 + y2 - 5x – 6y = 0
2
2
c) x + y + 5x – 6y = 0
d) x2 + y2 + 5x + 6y = 0
22. The equation of the radical axis of the circles 7x2 + 7y2 – 7x + 14y +18 = 0 and
4x2 + 4y2 – 7x + 8y + 20 = 0 is
a) 21x + 64 = 0
b) 21x – 68 = 0
c) 21y – 61 = 0
d) 21x + 68 = 0
23. The locus of centres of family of circles passing through the origin and cutting the circle
x2 + y2 + 4x – 6y – 13 = 0 orthogonally is
a) 4x + 6y + 13 = 0
b) 4x – 6y + 13 = 0
c) 4x + 6y – 13 = 0
d) 4x – 6y –13=0
2
24. The slope of the radical axis of the circles x + y2 – 3x – 4y+5=0 and 3x2 + 3y2–
7x+8y+11=0 is
a)
1
3
b) 1
10
c) 1
2
d) 2
3
25. The locus of the centre of the circle which cuts the circles x2 + y2 + 4x – 6y + 9 = 0 and
x2 + y2 - 4x + 6y + 4 = 0 orthogonally is
a) 12x + 8y + 5 = 0
b) 8x + 12y + 5 = 0
c) 8x – 12y + 5 = 0
d) 12x – 8y – 5=0
26. The equation of the circle with centre (2, 3) and touching y – axis is
a) x2 + y2 + 4x + 6y + 9 = 0
b) x2 + y2 + 4x – 6y + 9 = 0
d) x2 + y2 - 4x – 6y – 9 = 0
c) x2 + y2 - 4x - 6y + 9 = 0
27. When 3x + 3y + 7 = 0 is reduced to the form x cos v + y sin v = p then the value of ‘p’ is
7
7
7
7
a)
b)
c)
d)
3
2 3
2 2
3 2
2
28. The value of O for which the lines 3x + 4y = 5, 5x + 4y = 4 and Ox + 4y = 6 meet at a point
is
a) 2
b) 1
c) 4
d) 3
29. The image of the point (4, -3) with respect to the line y = x is
a) (-4, -3)
b) (3, 4)
c) (-4, 3)
d) (-3, 4)
30. If the angle between the lines 3x + ky + 1 = 0 and 2x + 5y – 7 = 0 is
b) 7 or
a) 7
9
7
c) 7 or
9
7
S
then k =
4
d) 7 or
9
7
31. The angle between the lines x2 + 4xy + y2 = 0 is
a) 600
b) 150
c) 300
d) 450
2
2
32. If kx + 7xy + 3y + 8x + 14y + 8 = 0 represents a pair of straight lines then k =
a) 2
b) 3
c) -2
d) 1
33. If slope of one of the lines ax2 + 2hxy + by2 = 0 is three times the other then, h2 is
a) 4ab
b)
4ab
3
c) ab
d)
3ab
4
34. The product of perpendiculars drawn from the point (1, 2) to the pair of lines x2 + 4xy + y2
= 0 is
a)
9
4
b)
3
4
c)
9
16
d)
13
4
35. The distance between the pair of parallel lines x2 + 2xy + y2 – 6x – 6y + 8 = 0 is
2 2
1
b) 2 2
c) 2
d)
3
2
36. The perpendicular distance between the lines 5x + 12y – 20 = 0 and 5x + 12y + 110 = 0 is
a) 6
b) 10
c) 13
d) 26
37. The equation of the straight line passing through the origin and the point of intersection of
the lines x + 2y + 7 = 0 and 2x – 3y – 9 = 0 is
a) 23x – 3y = 0
b) 25x – 3y = 0
c) 23x + 3y = 0
d) 3x + 23y = 0
38. The co – ordinates of the foot of perpendicular from (0, 0) to the line x + y = 2 are
a) (2, -1)
b) (-2, 1)
c) (1, 1)
d) (1, 2)
a)
39. If the medians AD and BE of the triangle with vertices A(0, b), B(0, 0) and C(a, 0) are
mutually perpendicular after
a) b
2a
b) a
r 2b
c) b
2a
d) b
a
40. The ratio in which the line y = x divides the segment joining (2, 3) and (8, 6) is
a) 1 : 2
b) 1 : - 2
c) 1 : 3
d) 1 : - 3
3